Crossed squares and combinatorial homotopy (Q1320986)

We develop ideas of \textit{R. Brown} and \textit{J.-L. Loday} to obtain algebraic classifications of 4-dimensional connected CW-spaces and of the homotopy classes of maps from a 3-dimensional connected CW-space to an arbitrary connected CW-space. This generalizes results of \textit{J. H. C. Whitehead} [Bull. Am. Math. Soc. 55, 453-496 (1949; Zbl 0040.388)], and is a variant on work of \textit{H. J. Baues} [Combinatorial homotopy and 4- dimensional complexes (1991; Zbl 0716.55001)].